A von Neumann stability analysis is conducted for numerical schemes for the
full system of coupled, density-based 1D and 2D Euler equations, closed by
an isentropic equation of state. The governing equations are discretized on
a staggered grid, which permits equivalence to finite-volume discretization.
Presently, first-order accurate spatial and temporal finite-difference
techniques are analyzed. The momentum convection term is treated as
explicit, semi-implicit or implicit. Density upwind bias is included in the
spatial operator of the continuity equation. By combining the discretization
techniques, ten solution schemes are formulated. For each scheme, unstable
and stable regimes are identified through the stability analysis, and the
maximum allowable CFL number is predicted. The predictions are verified for
selected schemes, using the Riemann problem at incompressible and
compressible Mach numbers. Very good agreement is obtained between the
analytically predicted and ``experimentally'' observed CFL values for all
cases, thereby validating the analysis. The demonstrated analysis provides
an accurate indication of stability conditions for the Euler equations, in
contrast to the simplistic conditions arising from model equations, such as
the wave equation. [Preview Abstract]

Eruption of geothermally heated water from the hydrothermal vent in deep oceans of depth over 2,000 meters is numerically simulated. The hydrostatic pressure of water is assumed to be over 200 atmospheres, and temperature of heated water is occasionally more than $300^{\circ}$C. Under these conditions, a part of heated water can be in the supercritical state, and the physical properties can change significantly by the temperature. Particularly, thermal diffusivity at the critical temperature becomes so small which prevents heat diffusion and the temperature gradients can become high.
The compressible Navier-Stokes equations are solved using a method for the incompressible equations under the constant pressure. The equations are approximated by the multidirectional finite difference method, and for the highly-unsteady-flow computation, KK scheme is used to stabilize the high-accuracy computation. To treat high temperature gradients in the computation, the energy equation is solved which is derived by transformation of thermodynamic variable $\phi$ into $\varphi$ that is $\varphi=-{\rm sgn}\phi\cdot\log(1-\phi\cdot{\rm sgn}\phi)$. Solving the equation about $\varphi$ instead of $\phi$ allows the sharp boundaries of $\phi$ to be properly preserved in the computation. [Preview Abstract]

The topology and evolution of flow around a surface mounted cubical object in three dimensional channel flow is examined for low to moderate Reynolds numbers. Direct numerical simulations were performed via a home made parallel finite element code. The computational domain has been designed according to actual laboratory experimental conditions. Analysis of the results is performed using the three dimensional theory of separation. Our findings indicate that a tornado-like vortex by the side of the cube is present for all Reynolds numbers for which flow was simulated. A horse-shoe vortex upstream from the cube was formed at Reynolds number approximately 1266. Pressure distributions are shown along with three dimensional images of the tornado-like vortex and the horseshoe vortex at selected Reynolds numbers. Finally, and in accordance to previous work, our results indicate that the upper limit for the Reynolds number for which steady state results are physically realizable is roughly 2000. [Preview Abstract]

The observable divergence theorem enables a systematic derivation of high-wavenumber regularized PDEs from conservation laws. Application of this theorem to the conservation of mass, momentum, and energy produces the inviscidly regularized observable Euler equations or, after adding physical dissipation, the observable Navier-Stokes equations. This talk will first present the derivation of the observable Euler equations from basic principles and then we report results for performance of the observable Euler and observable Navier-Stokes equations in several canonical problems involving multi-dimensional shocks and/or turbulence and their interactions. The results were compared with several previously published data using Stan, Stan-I, hybrid, WENO, ADPDIS3D, and shock fitting techniques. The observable equations consistently performs as well as the best methods. [Preview Abstract]

Determining how unstable laminar flames transition from an initial perturbed planar flame to a cellular structure is an important step in understanding turbulent flame propagation and their physical mechanisms. While Direct Numerical Simulations of the turbulent reacting-flow equations complete with detailed chemical models would be ideal, the computational expense for such large scale simulations is prohibitive. To this end, tabulated chemistry models are used in this work to capture the important physical mechanisms of unsteady laminar flames. Two dimensional numerical simulations of lean hydrogen/air premixed flames are performed for a variety of domain sizes and grid resolutions. A one dimensional hydrogen/air flame serves as the initial profile, which is perturbed using a sinusoidal disturbance in the transverse direction. Additionally, detailed chemistry simulations are performed as a comparison metric for the tabulated chemistry results. Finally, the tabulated chemistry results are compared to experimental data of spherically expanding flames. [Preview Abstract]

Fluid motion in a cubical cavity geometry driven by a rotating lid was
simulated using OpenFoam software. The flow structure observed is compared
with cylindrical cavity driven by rotating lid and the evolution of the flow
with Reynolds number is presented. The critical Reynolds number for
transition to oscillatory flow is estimated. The flow structure around the
critical Reynolds number is visualized and the effects of parameters on the
structure is presented. [Preview Abstract]

We have developed a low Mach number hydrodynamics code appropriate for modeling diffusive mixing of an arbitrary number of fluids with different densities and transport properties. Our low Mach number formulation eliminates acoustic waves and allows for an advective CFL time step constraint. Unlike models for incompressible flow which eliminate acoustic waves by imposing that the divergence of the velocity be zero, in this formulation the divergence is determined by the mixing of the fluids. We couple the divergence constraint to an implicit viscosity treatment using a newly-developed staggered-grid, finite-volume Stokes solver with a projection-method based preconditioner. Our code supports multiple time-stepping schemes suitable for both inertial and large Schmidt number regimes. The code has been implemented in the highly-scalable BoxLib software framework publicly available at Lawrence Berkeley Laboratory. The code also contains modules for thermal fluctuations using stochastic forcing terms as proposed by Landau and Lifshitz. We have successfully used the code to replicate multi-mode instabilities observed in experiments. [Preview Abstract]

Obstructive sleep apnea(OSA) is a medical condition characterized by repetitive partial or complete occlusion of the airway during sleep. The soft tissues in the airway of OSA patients are prone to collapse under the low pressure loads incurred during breathing. The numerical simulation with patient-specific upper airway model can provide assistance for diagnosis and treatment assessment. The eventual goal of this research is the development of numerical tool for air-tissue interactions in the upper airway of patients with OSA. This tool is expected to capture collapse of the airway in respiratory flow conditions, as well as the effects of various treatment protocols. Here, we present our ongoing progress toward this goal. A sharp-interface embedded boundary method is used on Cartesian grids for resolving the air-tissue interface in the complex patient-specific airway geometries. For the structure simulation, a cut-cell FEM is used. Non-linear Green strains are used for properly resolving the large tissue displacements in the soft palate structures. The fluid and structure solvers are strongly coupled. Preliminary results will be shown, including flow simulation inside the 3D rigid upper airway of patients with OSA, and several validation problem for the fluid-structure coupling. [Preview Abstract]

Finite volume simulations ranging from RANS to LES inherently require some discretization of the fluid region being examined, which is in many ways dictated by the numerics employed to represent Navier-Stokes. However, for generic finite volume codes, the presence of poor quality elements can lead to difficulty in obtaining a converged solution and, perhaps even worse, significant non-physical artifacts in a converged solution. A fundamental set of examples in two and three dimensions will be presented in order to demonstrate these effects and how to avoid them. Additionally, results for a benchmark geometry from a case study on grid effects will also be discussed. [Preview Abstract]

Many current multiscale methods are based on Eulerian descriptions, which have well-known difficulties when applied to problems of large material deformation and history dependency. Unfortunately, many problems requiring the consideration of multiscale and non-equilibrium thermodynamic effects are in this category.
In this talk, a general multiscale approach is introduced to study material responses at different scales. The up-scaling approach uses the ensemble averaging technique. The required closures for the averaged equations are expressed in terms of lower scale quantities, which can be evaluated directly using numerical simulations following the motion of the material. The required history tracking can be achieved efficiently using the dual domain material point (DDMP) method because of the Lagrangian nature of the material points.
The DDMP method requires only communications between material points and mesh nodes and no communication between material points. Therefore the response of the material represented by each material point can be numerically simulated independently in parallel computers with high efficiency. Applications of this approach to materials undergoing rapid and large deformation are demonstrated.
[Preview Abstract]